What logic gate produces an output that is true only if at least one input is false?

The correct choice is NAND because it specifically generates an output that is true except when all of its inputs are true. To understand this better, consider that the NAND gate is the negation of the AND gate. The AND gate outputs true only when all its inputs are true. Thus, for a NAND gate, if any one input is false, the outcome will be true. In a two-input scenario, this means that if at least one of the inputs is false, the result from the NAND gate will also be true.

In contrast, NOR outputs true only when both inputs are false, AND produces true only when both inputs are true, and NOT simply inverts the input signal. This reasoning aligns perfectly with the functionality defined for the NAND gate, making it the correct answer.